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  • Open Access
  • © 2017

Error-Correction Coding and Decoding

Bounds, Codes, Decoders, Analysis and Applications

  • Deepens your understanding of a ubiquitous and important technology using simple examples and easy-to-understand language
  • Presents a balanced mix of theory and applications
  • Diversity of applications will equip the reader to work with many aspects of coding and decoding in the real world
  • Includes supplementary material: sn.pub/extras

Part of the book series: Signals and Communication Technology (SCT)

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Table of contents (20 chapters)

  1. Front Matter

    Pages i-xx
  2. Theoretical Performance of Error-Correcting Codes

    1. Front Matter

      Pages 1-1
    2. Bounds on Error-Correction Coding Performance

      • Martin Tomlinson, Cen Jung Tjhai, Marcel A. Ambroze, Mohammed Ahmed, Mubarak Jibril
      Pages 3-23Open Access
    3. Soft and Hard Decision Decoding Performance

      • Martin Tomlinson, Cen Jung Tjhai, Marcel A. Ambroze, Mohammed Ahmed, Mubarak Jibril
      Pages 25-41Open Access
    4. Soft Decision and Quantised Soft Decision Decoding

      • Martin Tomlinson, Cen Jung Tjhai, Marcel A. Ambroze, Mohammed Ahmed, Mubarak Jibril
      Pages 43-58Open Access
  3. Code Construction

    1. Front Matter

      Pages 59-59
    2. Cyclotomic Cosets, the Mattson–Solomon Polynomial, Idempotents and Cyclic Codes

      • Martin Tomlinson, Cen Jung Tjhai, Marcel A. Ambroze, Mohammed Ahmed, Mubarak Jibril
      Pages 61-99Open Access
    3. Good Binary Linear Codes

      • Martin Tomlinson, Cen Jung Tjhai, Marcel A. Ambroze, Mohammed Ahmed, Mubarak Jibril
      Pages 101-136Open Access
    4. Lagrange Codes

      • Martin Tomlinson, Cen Jung Tjhai, Marcel A. Ambroze, Mohammed Ahmed, Mubarak Jibril
      Pages 137-165Open Access
    5. Reed–Solomon Codes and Binary Transmission

      • Martin Tomlinson, Cen Jung Tjhai, Marcel A. Ambroze, Mohammed Ahmed, Mubarak Jibril
      Pages 167-179Open Access
    6. Algebraic Geometry Codes

      • Martin Tomlinson, Cen Jung Tjhai, Marcel A. Ambroze, Mohammed Ahmed, Mubarak Jibril
      Pages 181-203Open Access
    7. Algebraic Quasi Cyclic Codes

      • Martin Tomlinson, Cen Jung Tjhai, Marcel A. Ambroze, Mohammed Ahmed, Mubarak Jibril
      Pages 205-288Open Access
    8. Historical Convolutional Codes as Tail-Biting Block Codes

      • Martin Tomlinson, Cen Jung Tjhai, Marcel A. Ambroze, Mohammed Ahmed, Mubarak Jibril
      Pages 289-298Open Access
    9. Analogue BCH Codes and Direct Reduced Echelon Parity Check Matrix Construction

      • Martin Tomlinson, Cen Jung Tjhai, Marcel A. Ambroze, Mohammed Ahmed, Mubarak Jibril
      Pages 299-314Open Access
    10. LDPC Codes

      • Martin Tomlinson, Cen Jung Tjhai, Marcel A. Ambroze, Mohammed Ahmed, Mubarak Jibril
      Pages 315-354Open Access
  4. Analysis and Decoders

    1. Front Matter

      Pages 355-355
    2. An Exhaustive Tree Search for Stopping Sets of LDPC Codes

      • Martin Tomlinson, Cen Jung Tjhai, Marcel A. Ambroze, Mohammed Ahmed, Mubarak Jibril
      Pages 357-366Open Access
    3. Erasures and Error-Correcting Codes

      • Martin Tomlinson, Cen Jung Tjhai, Marcel A. Ambroze, Mohammed Ahmed, Mubarak Jibril
      Pages 367-398Open Access
    4. The Modified Dorsch Decoder

      • Martin Tomlinson, Cen Jung Tjhai, Marcel A. Ambroze, Mohammed Ahmed, Mubarak Jibril
      Pages 399-419Open Access
    5. A Concatenated Error-Correction System Using the \(|u|u+v|\) Code Construction

      • Martin Tomlinson, Cen Jung Tjhai, Marcel A. Ambroze, Mohammed Ahmed, Mubarak Jibril
      Pages 421-431Open Access

About this book

This book discusses both the theory and practical applications of self-correcting data, commonly known as error-correcting codes. The applications included demonstrate the importance of these codes in a wide range of everyday technologies, from smartphones to secure communications and transactions. Written in a readily understandable style, the book presents the authors’ twenty-five years of research organized into five parts:

Part I is concerned with the theoretical performance attainable by using error correcting codes to achieve communications efficiency in digital communications systems.

Part II explores the construction of error-correcting codes and explains the different families of codes and how they are designed. Techniques are described for producing the very best codes.

Part III addresses the analysis of low-density parity-check (LDPC) codes, primarily to calculate their stopping sets and low-weight codeword spectrum which determines the performance of th

ese codes.

Part IV deals with decoders designed to realize optimum performance.

Part V describes applications which include combined error correction and detection, public key cryptography using Goppa codes, correcting errors in passwords and watermarking.

This book is a valuable resource for anyone interested in error-correcting codes and their applications, ranging from non-experts to professionals at the forefront of research in their field.

This book is open access under a CC BY 4.0 license.

Authors and Affiliations

  • School of Computing, Electronics and Mathematics, Plymouth University, Plymouth, United Kingdom

    Martin Tomlinson, Marcel A. Ambroze

  • PQ Solutions Ltd, London, United Kingdom

    Cen Jung Tjhai

  • School of Computing, Electronics and Mat, Plymouth University School of Computing, Electronics and Mat, Plymouth, United Kingdom

    Mohammed Ahmed

  • Satellite Applications and Development, Nigeria Communications Satellite Ltd., Abuja, Nigeria

    Mubarak Jibril

About the authors

Professor Martin Tomlinson is best known for inventing the Tomlinson-Harashima pre-coding technique. He received his PhD on the subject of adaptive equalisation for data transmission from Loughborough University in 1970. He later worked at Plessey Telecommunications Research Ltd. in the field of digital and satellite transmissions and then at the Satellite Communications Division of the Royal Signals and Radar Establishment (RSRE) (now Qinetiq). He was also the project manager for the communications aspects of the NATO IV satellite before joining the University of Plymouth as the head of the Communication Engineering Department in 1982. Professor Tomlinson has published 186 papers, holds 33 patents and is a well known member of several professional institutes and societies. He is Emeritus Professor of Communications at the University of Plymouth and is also Chief Scientific Officer of Post-Quantum, a company specializing in secure communications and cryptographic products. 

Dr. Cen Jung Tjhai is an expert in error correcting codes, cryptography, digital signal processing and wireless communications. He is Chief Technology Officer at Post-Quantum and is responsible for secure messaging, authentication and blockchain product developments. Prior to this, he was a lecturer at the University of Plymouth and carried out research in a number of government projects in secure digital signal processing and cyber security. Dr. Tjhai has published over 30 papers and currently holds 16 patents. 

Dr. Adrian Ambroze was awarded his PhD in Turbo Codes from the University of Plymouth in 2000 and currently holds the position of Lecturer in Digital Communications. He is an expert on Turbo codes, LDPC codes and iterative decoders. He is a member of the Institute of Electrical and Electronics Engineers (IEEE) and a reviewer for a number of the institute’s publications as well as for the Engineering and Physical Sciences Research Council (EPSRC). Dr. Ambroze

has published over 50 papers and currently holds 6 patents.

Dr. Zaki Ahmed completed his BEng, MEng and PhD degrees at the University of Plymouth (1996–2003) and was appointed as a permanent member of staff in 2001. He currently holds the position of Associate Professor in Information Technology and is a fellow of the Japanese Society for the Promotion of Science (FJSPS) and the Higher Education Academy (FHEA). Dr. Ahmed is also a respected member of the Institute of Electrical and Electronics Engineers. He is an expert in the areas of coding bounds and constructions of best known, error correcting codes. Dr. Ahmed has published over 70 papers and currently holds 10 patents.  

Dr. Mubarak Jibril received a Bachelor of Engineering in Electrical and Electronic Engineering from Bayero University Kano in 2005. At the University of Plymouth he completed his MSc in Digital Communications and Signal Processing in 2008 and was awarded his PhD for research into Alg

ebraicGeometry Codes in 2011. He is currently employed by the Nigerian Communications Satellite Company Limited in Abuja, Nigeria. Dr. Jibril is an expert in Algebraic Geometry (AG) error correcting codes and has published several journal articles on Goppa codes and new, best known, AG codes. 



Bibliographic Information

  • Book Title: Error-Correction Coding and Decoding

  • Book Subtitle: Bounds, Codes, Decoders, Analysis and Applications

  • Authors: Martin Tomlinson, Cen Jung Tjhai, Marcel A. Ambroze, Mohammed Ahmed, Mubarak Jibril

  • Series Title: Signals and Communication Technology

  • DOI: https://doi.org/10.1007/978-3-319-51103-0

  • Publisher: Springer Cham

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s) 2017

  • Hardcover ISBN: 978-3-319-51102-3Published: 02 March 2017

  • Softcover ISBN: 978-3-319-84567-8Published: 13 July 2018

  • eBook ISBN: 978-3-319-51103-0Published: 21 February 2017

  • Series ISSN: 1860-4862

  • Series E-ISSN: 1860-4870

  • Edition Number: 1

  • Number of Pages: XX, 522

  • Number of Illustrations: 52 b/w illustrations, 82 illustrations in colour

  • Topics: Communications Engineering, Networks, Computer Communication Networks, Coding and Information Theory, Algorithms

Buy it now

Buying options

Softcover Book USD 59.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 59.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access